Multi-type branching in varying environment

by J.D.Biggins H.Cohn and O.Nerman. )

Stoc. Proc. Appl., (1999) 83, 357-400.

1991 Mathematics Subject Classification: 60J80

Abstract

This paper considers the asymptotic theory of the varying environment Galton-Watson process with a countable set of types. This paper examines the convergence in $L_{p}$ and almost surely of the numbers of the various types when normalised by the corresponding expected number. The harmonic functions of the mean matrices play a central role in the analysis. Many previously studied models provide particular cases.

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